Despite sweeping pessimism about the nation’s fortunes and his own sliding approval ratings, President Obama leads potential Republican rivals Mitt Romney and Rick Perry in hypothetical general-election matchups, according to a new TIME poll.

Obama leads Romney, the former Massachusetts governor who sits atop the GOP presidential field, 46% to 43% among likely voters. The President has opened a double-digit lead over Perry, 50% to 38%, highlighting concerns percolating through the GOP that the Texas governor would face a steep uphill climb should he capture the nomination. Obama also boasts a 49%-to-37% edge over businessman Herman Cain, whose strong Tea Party support has propelled him toward the top of Republican ranks in recent weeks.

In each case, the President was buoyed by his performance among female voters. Women prefer Obama over Romney by 8 percentage points (49% to 41%), over Perry by 17 points (53% to 36%) and over Cain by 21 points (53% to 32%).

Obama’s strength in head-to-head matchups with his potential Republican rivals belies his own shaky footing with a weary electorate. Just 44% of voters approve of the President’s performance, a slip of 4 points since a similar poll was conducted in June. Four out of five respondents say the U.S. has veered off-track, and 71% think the country’s clout in the world is waning. A scant 5% report feeling positive or unconcerned about the state of the nation.

The President’s positive personal qualities have cushioned voters’ frustration with the sagging U.S. economy, the exodus of capital to overseas markets and the declining value of the dollar. Most voters see Obama as tough enough to shepherd the U.S. through this rough patch (50% to 44%) and empathetic (59% to 37%) to the concerns of Americans like themselves. By a 48%-to-37% margin, respondents consider him a better President than his predecessor, George W. Bush, who won a hard-fought battle for a second term amid falling approval ratings and an opposition galvanized by the war in Iraq.

For Democrats, the silver lining in a gloomy series of electoral rebukes and legislative setbacks is that voters remain partial to their chief economic principles, at least compared with the alternatives. Forty-two percent of respondents say they place greater trust in the Democratic Party to deal with the nation’s problems, compared with the 31% who side with Republicans. In particular, some two-thirds of those surveyed say they prefer the Democrats’ blueprint for trimming the federal deficit — a mix of spending cuts and tax hikes — to the GOP prescription, which would solely slash spending. At the same time, more voters think reducing spending is a better way to juice the moribund economy than an additional round of stimulus, the approach advocated by liberal economists.

The survey also revealed that respondents have a better impression of the left-leaning protest movement known as Occupy Wall Street than they do of the Tea Party movement. Fifty-four percent of respondents harbor a positive view of the burgeoning protest movement, well above the 23% with a negative opinion. By contrast, just 27% of those surveyed have favorable views of the Tea Party, while 65% say its impact on U.S. politics since its inception in 2009 has been negative or negligible.

Those results reflect a strain of economic populism common to the new movement’s backers. Among those respondents familiar with Occupy Wall Street, nearly 80% argue that the wealth disparity in the U.S. has grown too large, and 68% say the rich should pay more taxes. Even so, this cohort is aware of the challenges facing the movement. Fifty-six percent predict that Occupy Wall Street will have little impact on American politics, and another 9% say its effect will be negative.

The poll, conducted for TIME by Abt SRBI, surveyed 1,001 adults — 83% of whom described themselves as likely voters — between Oct. 9 and 10.